The People’s Climate March in New York City on Sept. 21 promised to be “the largest climate march in history.” If media coverage is any indicator, it was. According to Google Trends, news headlines in September mentioned the phrase “climate march” more than any time in the history of the service’s data collection.

But how many people attended the event? We don’t exactly know. A LexisNexis search shows that 2,021 articles written on or after Sept. 21 mention the words “People’s Climate March.” The New York Times wrote that 311,000 people were there. The Wall Street Journal took a more skeptical view, saying that “hundreds of thousands” marched, while citing the march organizers’ estimate of nearly 400,000. Meanwhile, the Associated Press was perhaps too conservative, going no further than saying that “tens of thousands” showed up. Aerial footage made clear that dozens of city blocks were packed with marchers.

All these numbers (with the exception of the AP’s) came from the march organizers — at 3 p.m. on the day of the event, they released their official crowd count of “over 310,000.” But just hours later, they released a new figure of 400,000 — a 29 percent increase from the original count. Neither of those numbers was based on a rigorous methodology.

Organizers advertised that their method relied “on a crowd density analysis formula developed by a professor of game theory and complex systems at Carnegie Mellon University” and that it “calculates the average density of the march crowd over specific intervals, factoring in the surface area covered by the crowd and the speed and duration of the march.”

But that professor at Carnegie Mellon had no background in crowd counting. His name is Russell Golman. He teaches quantitative social sciences and heard that the People’s Climate March was looking for someone to help get an estimate of attendees. “So I just reviewed some online literature and gave them a few different options,” Golman said in an interview Monday. But, he said, “I’ve never done crowd counting before.”

After doing his research, Golman offered some ways for the organizers to get a count: estimate crowd size by measuring its density from above; put counters on the ground at various spots and extrapolate their counts given how long the march took; or do some combination of the two. Beyond that, he said, he wasn’t very involved in the process. “My understanding is that they intended to use both methods, but they ended up needing an estimate before the march was over,” he said.

The planners went with the density-from-above option. But they improvised a bit, according to Jamie Henn, the strategy and communications director at 350.org, one of the organizers of the march. “We added about 10 percent at the end to include the sidewalks that people had access to, and the side streets that people were using,” he said. “For example, labor unions rallied on Broadway, and they had about 10,000 people there.”

That’s how the 310,000 number was determined. But what about the 400,000? “After we put that number [310,000] out, we started getting radio calls from marshals along the routes that said that because the routes got so crowded, people had peeled off of Central Park West by the time we did our counts. … We didn’t crowd count, but from our people on the radio, it seemed like [400,000] is the count we got to,” Henn said.

When asked about the increased numbers, Golman said that he “was not involved with that” and that “311,000” — the number The New York Times used, citing organizers — “seems absurdly precise to me.”

Past marches have shown that crowd estimates are hard, with room for them to grow in step with feelings about the urgency of the cause. “The size of the crowd becomes a symbol of how important it is,” said Steven Doig, a professor at Arizona State University and a crowd-counting veteran who helped out with counts for Pope Benedict XVI’s U.S. appearances and President Obama’s first inauguration.

Disparate crowd counts aren’t uncommon. Just take a look at the controversies surrounding the crowd counts for the Million Man March in 1995, or Glenn Beck’s Restoring Honor rally in 2010. For both events, the “official” crowd count touted by the organizers was much higher than the count released by outside entities. After the Million Man March, the Nation of Islam (who estimated more than 1 million participants) threatened to sue the National Park Service, whose estimate was 400,000.

Doig laid out the ideal way to count: “You have some sort of aerial imagery that gives you a sense of where the crowd was and the density — and the density is the key for it,” he said. “If the march was 20 blocks long, that doesn’t necessarily mean that all 20 blocks were filled sidewalk to sidewalk, shoulder to shoulder.”

You would then measure the width and the length of the 20 blocks (Doig recommended using Google Maps) and get a rough measure of the density. There are basic guides: If people can reach their arms out and touch the shoulders of other people on all four sides (the approximate distance that you would need to be able to march), then the density is roughly one person per 10 square feet. So you would calculate different sections of the march according to density (the front of the march is usually much more dense than the back) and combine them. “Then you would have the realistic kind of estimate of how many people might possibly be there,” Doig said.

For an on-the-ground count, the preferred method is to enlist a team of counters and dispatch them at different points along the march route, counting how many people pass in a given increment of time, such as 30 seconds. After the march is over, the counters then add their counts accordingly, use those numbers to estimate how many people passed in the time intervals when the counters weren’t counting, and then combine counts for a final estimate. Using this method, two crowd counters calculated that about 125,000 people were present at the climate march.

Doig has used both methods at various events, and almost always comes out with a drastically lower number than the alternative count. The most dramatic instance of this, he said, was a 2010 labor rally in Lisbon, Portugal, where he counted “a generous 8,000.” The organizers’ projected count was 100,000.

Doig is almost certain that the count at the climate march is no different from those of past marches. “With events where there’s an agenda, no matter what the agenda is, if there isn’t a turnstile, then fiction is often involved in it,” he said.

Disclosure: The editor of this article participated in the People’s Climate March in New York City.